In this post, we will discuss the basics of the complex number, representation of complex numbers on the complex plane, polar and Euler form, and the triangle inequality. In each video lecture, we have discussed the examples along with the concept to illustrate each topic effectively. You can brush up your knowledge through the basic mathematics course and proceed to the next step to learn advanced maths.
Complex number basics
A number which can be expressed as (x + i y) is called the complex number. Where x is the real part of the complex number, y is the imaginary part of the complex number and i is the square root of -1. We denote the complex number by letter z. we represent complex numbers on the complex plane or Argand plane and the diagram is called Argand diagram. With the help of the Argand diagram, we can find the argument as well as the modulus of the complex number. Watch the video lecture to learn about the complex number and its representation on the complex plane.
Polar and Euler form of complex number
When we express the complex number in terms of its direction and modulus value, we get the polar form. And when we express the complex number in the exponential form, we get the Euler form. We denote modulus of a complex number by r and direction by symbol theta, where theta is the angle made by complex number with the real axis. Watch the video lecture to grab the topic of the polar and Euler form of a complex number.
We know that, for any triangle, one side cannot exceed the sum of the other two sides. This concept is used to derive the triangle inequality in the complex number. Watch the topic through the video lecture given below.
That is all for this post. You can get the full playlist of higher engineering maths by following the colored link and you can also ask your doubts through the comment section below or by contacting us. We will try to reply as soon as possible.